What is the integral of (sin(2x))/((1-cos^2(x))) ?

The integral of (sin(2x))/((1-cos^2(x))) is ln(sin^2(x))+C

Popular >

integral of (sin(2x))/((1-cos^2(x)))

\int \frac{sin ( 2 x )}{( 1 - cos ^{2} ( x ) )} d x

ln (sin^{2} (x)) + C

Solution steps

\int \frac{sin ( 2 x )}{1 - cos ^{2} ( x )} d x

Rewrite using trig identities

= \int \frac{sin ( 2 x )}{sin ^{2} ( x )} d x

Apply u-substitution

: \int \frac{1}{u} d u

= \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = sin^{2} (x)

= ln sin^{2} (x)

Apply absolute rule:

x^{2} = x^{2}

, assuming

x \in R

sin^{2} (x) = sin^{2} (x)

= ln (sin^{2} (x))

Add a constant to the solution

= ln (sin^{2} (x)) + C

x^{2} + 2 x - 1

\int \frac{9 ^{2 x + 5}}{3} d x

\int_{3}^{6} 1 + x^{4} + 2 x^{2} d x

\frac{d}{d x} ((x^{2} + 5 x - 6) (x^{3} + 5 x - 8))

\int (3 x - 2)^{2} d x

What is the integral of (sin(2x))/((1-cos^2(x))) ?
The integral of (sin(2x))/((1-cos^2(x))) is ln(sin^2(x))+C